Time Is Space

Time Is Space | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 31 March 2026 V1 Latest version Share on Time Is Space Author : Michael Timothy Bennett 0000-0001-6895-8782 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.177499234.48752073/v1 326 views 134 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract Complexity theory carves the world into time and space. Here I prove the distinction is an artefact of description, not of computation. I define a formalism in which representations are physically embodied and thus finite. In that setting, time is sequentially realised distinction and space is simultaneously realised distinction. Both are counts of a single underlying resource I call tone. Space is a chord of simultaneous tones. Time is an arpeggio of sequential tones. I prove two identities. Cumulative space through a bounded window is exactly ordinary space in a lifted vocabulary. Elapsed time is exactly a space count in a tick vocabulary. A bounded Turing-machine reconstruction recovers classical machine time and used-space as instances of this single resource. An exact block-product theorem further shows that literal-count simplicity and weakness (the count of compatible completions) coincide only when representational blocks are perfectly uniform. Real machines almost never satisfy this condition. The standard complexity classes are not affected. But time and space are not carved into computation. You carved them in when you chose a vocabulary. Supplementary Material File (time is space.pdf) Download 412.15 KB Information & Authors Information Version history V1 Version 1 31 March 2026 Copyright This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License Keywords abstraction computational complexity levels of description philosophy of computation space complexity time complexity Authors Affiliations Michael Timothy Bennett 0000-0001-6895-8782 [email protected] View all articles by this author Metrics & Citations Metrics Article Usage 326 views 134 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Michael Timothy Bennett. Time Is Space. Authorea . 31 March 2026. DOI: https://doi.org/10.22541/au.177499234.48752073/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. 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